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If you understand DFT, it should be very easy to understand FFT. It's the same thing but with an infinite-dimensional vector space. The fact that it's a vector
by 4ad 11y ago
If you understand DFT, it should be very easy to understand FFT. It's the same thing but with an infinite-dimensional vector space. The fact that it's a vector space is the important thing. The infinite dimensionality is relatively a minor detail.
- ablatner 11y agoNo that's not right. The FFT is not infinite dimensional. It's the same dimension as whatever length FFT you take. The FFT is just a set of algorithms for computing the DFT. In general they work by recursively decomposing an N-length DFT into shorter length DFT's. The DTFT on the other hand is "infinite" dimensional in that it takes an infinite time series as input and outputs a continuous spectrum with period of 2pi.
- 4ad 11y agoSorry, This is embarrassing, I must have not drank my coffee... Of course you are right.
- blt 11y agoI was talking about the O(n log n) algorithm that computes the DFT.
- 4ad 11y agoYeah, see my other comment.